# How do you find the center and radius of a circle using a polynomial x^2 + y^2 - 6x + 10y + 9 = 0?

##### 1 Answer
May 24, 2018

Center is at $\left(3 , - 5\right)$ and radius is $r = 5$ unit.

#### Explanation:

${x}^{2} + {y}^{2} - 6 x + 10 y + 9 = 0$ or

$\left({x}^{2} - 6 x\right) + \left({y}^{2} + 10 y\right) = - 9$ or

$\left({x}^{2} - 6 x + 9\right) + \left({y}^{2} + 10 y + 25\right) = 34 - 9$ or

${\left(x - 3\right)}^{2} + {\left(y + 5\right)}^{2} = {5}^{2}$. The center-radius form of the circle

equation is (x – h)^2 + (y – k)^2 = r^2, with the center being at

the point $\left(h , k\right)$ and the radius being $r$. Center is at

$\left(3 , - 5\right)$ and radius is $r = 5$ unit.

graph{x^2+y^2-6 x+10 y+9=0 [-20, 20, -10, 10]} [Ans]